Here's a jump rope rhyme that mentions police officers that I remember from my childhood. Fwiw, I don't remember "I Don't Want To Go To Macys/Mexico" from my childhood:

Policeman Policeman Do Your Duty
Policeman, Policeman, do your duty.
Here comes Debby
An American beauty,
She can wiggle
She can wobble
She can do the split.*
But I betcha five dollars
She can't do this.
Lady on one foot, one foot, one foot
Turn all around, around, around.
Lady on two foot, two foot, two foot
Touch the ground, the ground, the ground.
Lady on three foot, three foot, three foot
Say your prayers, your prayers, your prayers.
Lady on four foot, four foot, four foot
Jump right out.
-Azizi Powell, Atlantic City, New Jersey, mid 1950s.

*Substitute the name or nickname of the girl who is jumping rope. "Do the split" was sometimes given as "do the flip" {meaning the acrobatic movements}. However, these words were changed to "do the twist" in the 1960s when that dance became popular. Btw, I've also seen this rhyme written as "Mailman, Mailman Do Your Duty" and "Postman, Postman, Do your Duty".

**

Here's a variat form of that rhyme that I collected from my daughter. She performed it as a jump rope rhyme in the 1980s, Pittsburgh, Pennsylvania:

Police Lady Police Lady Do Your Duty
Police lady, police lady. Do your duty.
Here comes Keisha
with ah African booty.
She can wiggle.
She can wobble.
She can do the split.
But I betcha five dollars
She can't do this.
Lady on one foot, one foot, one foot
Turn all around, around, around.
Lady on two foot, two foot, two foot
Touch the ground, the ground, the ground.
Lady on three foot, three foot, three foot
Say your prayers, your prayers, your prayers.
Lady on four foot, four foot, four foot
Jump right out.
-TMP; Pittsburgh, Pennsylvania, mid 1980s

*Substitute jumper's name or nickname. Btw, "an African booty" means "a big butt". Here's what I believe are the meanings of "one foot, "two foot" etc. Someone please correct me if I'm misremembering this: "One foot" means hopping. One foot touches touching the ground when you jump. Two foot" is jumping with both feet off the ground. "Three foot" is two hands touching the ground and then one foot . "Four foot" is jumping with both hands and both feet touching the ground.

I think the change from "policeman" to "police lady" is significant. When I was growing up, there were no female police officers that I knew of.

Here's a challenge to Mudcat members and guests: Name a folk song or any other song that mentions a female police officer.

I betcha can't.